Geodesic
A relaxation scheme for inviscid flows under gravitational influence
Jeaniffer Vides1 ; Edouard Audit2 ; Boniface Nkonga3
1 Inria, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France
2 CEA, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France
3 Université de Nice-Sophia Antipolis, UMR CNRS 7351 & Inria Sophia Antipolis, France
ESAIM. Proceedings, Tome 45 (2014), pp. 523-532.

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Many astrophysical flows are modeled by the Euler equations with gravity source terms derived from a potential, the evolution of which is described by a Poisson equation. Several gravitational flows reach equilibrium states that are necessary to preserve in the numerical formulation. In this paper, we present the derivation of the relaxation model ? , in which the pressure is a supplementary variable and the Poisson equation is transformed into a hyperbolic equation with a penalty parameter. The corresponding scheme is obtained in the limit as the parameter tends to zero. The proposed Riemann solver, implemented in the software HERACLES ? , provides better robustness compared to other approaches available in the same software and is capable of preserving gravitational equilibria when required. Several numerical tests and results are presented, as well.
DOI : 10.1051/proc/201445054

Jeaniffer Vides 1 ; Edouard Audit 2 ; Boniface Nkonga 3

1 Inria, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France
2 CEA, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France
3 Université de Nice-Sophia Antipolis, UMR CNRS 7351 & Inria Sophia Antipolis, France 
@article{EP_2014_45_a54,
     author = {Jeaniffer Vides and Edouard Audit and Boniface Nkonga},
     title = {A relaxation scheme for inviscid flows under gravitational influence},
     journal = {ESAIM. Proceedings},
     pages = {523--532},
     publisher = {mathdoc},
     volume = {45},
     year = {2014},
     doi = {10.1051/proc/201445054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445054/}
}
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Jeaniffer Vides; Edouard Audit; Boniface Nkonga. A relaxation scheme for inviscid flows under gravitational influence. ESAIM. Proceedings, Tome 45 (2014), pp. 523-532. doi : 10.1051/proc/201445054. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445054/

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